Research On The Existence Of Positive Ground State Solution To A Nonlinear P-Kirchhoff Type Problem

In this paper, we study the existence of positive ground state solution to the following p-Kirchhoff type problem where a, b> 0 are constants, p > 0, p + p/2p+1-N?s<p* (?)NP/N-p, N > p, ?pu=div(|?u|p-2?u) is the p-Laplacian of u. V : RN ?R is a potential. Under certain assumptions on the potential V, we show that the equation (0.1) has a positive ground state solution by using free variational methods and a global compactness lemma. The main results Theorem 1.1 and Theorem 1.2 of this paper extend the range of the s and N from N < s <p*,N? p+1 in [20] to p+p/2p+1-N?s<p*,p<N<p* under which there exists a positive ground state solution to the p-Kirchhoff type problem(O.1).